On the Spectrum of Trees
碩士 === 國立中央大學 === 數學研究所 === 97 === In 1984, Godsil defined the Bethe tree $B(k,n)$ and showed the spectral radius $ ho$ of $B(k,n)$ satisfies $ ho<2sqrt{k}$. In this thesis, we find the spectrum of $B(k,n)$. With this spectrum, we also show the spectral radius $ ho$ of a tree $T$ satisfies $$sqr...
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2009
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ndltd-TW-097NCU054790292019-05-15T19:27:42Z http://ndltd.ncl.edu.tw/handle/5kkt76 On the Spectrum of Trees Li-Cheng Hsu 許立成 碩士 國立中央大學 數學研究所 97 In 1984, Godsil defined the Bethe tree $B(k,n)$ and showed the spectral radius $ ho$ of $B(k,n)$ satisfies $ ho<2sqrt{k}$. In this thesis, we find the spectrum of $B(k,n)$. With this spectrum, we also show the spectral radius $ ho$ of a tree $T$ satisfies $$sqrt{Delta}leq ho< min{2sqrt{Delta-1}cos{(frac{pi}{D+2})},2sqrt{Delta}cos{(frac{pi}{r+2})}},$$ where $D$,$r$,$Delta$ are the diameter, radius, and the maximum degree of $T$ respectively. The equality of lower bound holds only when $T=K_{1,Delta}$. Hua-Min Huang 黃華民 2009 學位論文 ; thesis 26 en_US |
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en_US |
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Others
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NDLTD |
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碩士 === 國立中央大學 === 數學研究所 === 97 === In 1984, Godsil defined the Bethe tree $B(k,n)$ and showed the spectral radius $
ho$ of $B(k,n)$ satisfies $
ho<2sqrt{k}$.
In this thesis, we find the spectrum of $B(k,n)$. With this spectrum, we also show the spectral radius $
ho$ of a tree $T$ satisfies
$$sqrt{Delta}leq
ho< min{2sqrt{Delta-1}cos{(frac{pi}{D+2})},2sqrt{Delta}cos{(frac{pi}{r+2})}},$$
where $D$,$r$,$Delta$ are the diameter, radius, and the maximum degree of $T$ respectively. The equality of lower bound holds only when $T=K_{1,Delta}$.
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| author2 |
Hua-Min Huang |
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Hua-Min Huang Li-Cheng Hsu 許立成 |
| author |
Li-Cheng Hsu 許立成 |
| spellingShingle |
Li-Cheng Hsu 許立成 On the Spectrum of Trees |
| author_sort |
Li-Cheng Hsu |
| title |
On the Spectrum of Trees |
| title_short |
On the Spectrum of Trees |
| title_full |
On the Spectrum of Trees |
| title_fullStr |
On the Spectrum of Trees |
| title_full_unstemmed |
On the Spectrum of Trees |
| title_sort |
on the spectrum of trees |
| publishDate |
2009 |
| url |
http://ndltd.ncl.edu.tw/handle/5kkt76 |
| work_keys_str_mv |
AT lichenghsu onthespectrumoftrees AT xǔlìchéng onthespectrumoftrees |
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1719089119754190848 |